-
>> So do you want to look at
some of the student work?
-
>> Yes, let's take a look.
-
>> And how do you want to sort them?
-
>> Yeah, so we have two piles right now.
One is their individual papers,
-
where they were asked to
make a conjecture,
-
to consider the data and have their
own noticings and wonderings about it,
-
and then to come back.
So I'd like to see if they,
-
if any of them revised
their original thinking.
-
>> Okay.
-
>> So maybe we can--
>> We'll split it--
-
>> You and I can just do like a quick--
-
>> Yeah.
>> Flip to see if ...
-
>> If there's anything different?
>> If there's anything different.
-
And then--
>> And by different, do you mean
-
the number or by the model?
-
>> I'm thinking the number.
>> Okay.
-
>> What I'm seeing so far is
that they're all putting 2.
-
>> Mm-hmm. [affirmative]
>> Because they have that data.
-
Because they have that
information from the table,
-
and, so they're just saying,
"Oh, okay, it's from the table.
-
So that must be correct."
-
>> Not all of them.
>> No?
-
>> Nope. Some of them are
consistent with their solution from
-
their original conjecture,
despite the fact that it was wrong.
-
And then do you want to
sort them for the ones
-
that made the adjustment
to the true number?
-
So I have some that have ...
They changed their opinion.
-
>> Mm-hmm. [affirmative]
>> But it went from 5 to 1.
-
>> Mm-hmm. So, but even
those that changed it to the 2,
-
I think that they made that change
because-- that's what the table says.
-
>> Right.
>> It's the maximum.
-
>> But, there are some
that still changed it to a 1.
-
>> I have some that
changed it to a 1 as well.
-
> Okay, so let's look at those
differently then, I guess.
-
>> Okay.
> Ooh, I got a 4.
-
>> And that was left off of the--
boxes, the one with the one cut.
-
So maybe they're thinking,
the smaller the cut.
-
>> Well, there are also some
here with 4s.
-
>> That changed to a 4?
>> Yes.
-
>> Oh, interesting.
>> Yes.
-
I'm trying to see if they're
at the same table.
-
No.
>> No.
-
These two were up at this table.
>> Yeah.
-
>> Where was Antonio?
Is he at the back corner?
-
Does he wear glasses?
>> No, Antonio has curly hair.
-
He was sitting up here, I think.
>> Oh, okay.
-
>> Emilio has glasses, so he was ...
>> Oh, yeah. Mm-hmm.
-
Okay.
-
>> So you did have a
number of them then.
-
If you want to measure that,
your stack of the ones who changed their--
-
>> Who changed their--
>> Opinion.
-
>> Opinion. So that's the majority.
-
So 16.
>> Mm-hmm.
-
>> Out of ... Who was in here?
-
Maybe--
>> 31.
-
>> 36. 31?
>> Or 35.
-
>> 30...
>> You're right.
-
-- 8 times 4 ... 30 ... 31 students.
>> 31. So 16 out of 31
-
changed their conjecture after
looking at the table.
-
>> Mm-hmm.
>> And these students changed
-
it to 2 centimeters based on
what they see in the table.
-
>> Mm-hmm. And do you think
that if you hadn't taken that pause,
-
the thought process of making a conjecture
and revising it would have come naturally?
-
>> I don't think all students
would do that naturally.
-
No. I'm actually realizing I have a ...
That's one in there.
-
>> And so, what do you think was the
move that you made as a teacher
-
to help them get to this space?
Because we are talking about now
-
the majority of the students.
>> Mm-hmm.
-
Well, I think just that the design
of the lesson to have a pause
-
and to ask them to revisit
and invite them to revise.
-
>> Mm-hmm.
>> I think just that practice of
-
slowing down what we're doing
so that students have the time
-
to sort of be metacognitive about their
own learning process, you know?
-
That's what -- that’s
what strong thinkers do
-
is we think about, and we revise,
thinking as we go.
-
>> Mm-hmm.
>> Right?
-
I'm not calling myself a strong thinker.
I'm just saying the royal we, you know?
-
I put this one on top because
I'm interested to read. He says,
-
"I think it will be a 2-centimeter cut,
because the smaller the cut size,
-
"the greater the length and width
even though the height is small."
-
>> Mm-hmm.
>> So with this student,
-
I don't recognize this handwriting--
-
or the name. Who is that?
>> Jeannette.
-
>> Oh.
>> Linette, sorry.
-
>> Linette. Oh, so she's really
trying to reason through
-
why that might provide
the greatest volume.
-
>> Mm-hmm.
>> Which I don't see is necessarily true
-
of all of the students who did revise
their thinking. I see more frequently,
-
“I think the 2-centimeter cut will
maximize the volume because ...”
-
>> I'm looking at.. Yeah.
>> It's the one that
-
has the greatest volume,
you know? And there I see
-
maybe three who are really thinking
about, why is it 2, you know?
-
and relating it to the length and
the width that are also considered.
-
>> But I think you gave them
the opportunity in the beginning
-
to justify their original thinking.
>> Mm-hmm.
-
>> And, so that there were
some ideas put out there.
-
Because some of the students were
talking about the area of the base --
-
>> Of the base. That's right.
>> And were being considerate of that.
-
>> Mm-hmm.
>> And then I also heard
-
another student that was
talking about the same idea
-
about just using a 1,
because that leaves me
-
with the most on the bottom--
>> Base area.
-
>> Yeah.
>> Right, yeah.
-
Right, and I think also,
you know, often in math class,
-
teachers and students are about
getting answers and moving through content
-
at a pace. And so, I think anything
that slows that process down
-
helps learners step up and have
the opportunity to really learn
-
instead of just have
things thrown at them.
-
>> Mm-hmm.
